I noticed that the compositing is applied after the image is rendered. Does this mean that when working with an 8-bit Output that the compositor can affect image quality negatively? (i.e. artifacts like banding etc.)
No, the compositor will not degrade rendered images. The compositor works with 32bit float precision, in scene referred linear (meaning that there is way more information that what can be displayed in the monitor).
Of course, there could be intentional or unintentional degrading in the compositor caused by incorrectly connected nodes and/or poor judgement by the user.
A likely source of image degradation is the use of highly compressed images in lossy compression schemes (like jpeg or mpeg), in which the the original image will suffer corruption with each subsequent cycle of decompression and re-compression.
As for Color Banding, it would happen when the image is saved to 8 bit formats, as this method of encoding cannot resolve subtle color gradation with only 255 levels for each color. Areas of similar colors, and dark, almost monochromatic gradients, will suffer greatly.
To disguise banding in the rendered image, use dithering.
Note that even if the image is saved as 16 bit or 32 bit per channel, it is possible that it cannot be displayed at a better quality: Most monitors display only 8 bits per channel (and some even less than that). Banding then is inevitable (just pause any of your favorite movies during streaming and you will see what I'm talking about). Banding might disappear if the higher bit depth images are displayed properly in a 10 bit monitor or better (retina display or any professional grade monitor or video projector)
As for if I've tested it - yes. I've worked with arri and r3d footage converted to 16 bit half float exr to import into blender and am noticing a degradation on the export. I'm noticing it on 8 bit mxf files. Am noticing it on prores smpte 2084 1000 nits material. The issue is consistent - so my query is IF the compositor's export is degrading the material in any way or if it's being affected on the import. The primary reason for this is that if there is a degradation in footage, it renders B3D's compositor useless for production VFX as it would kick back every time from DI due to affecting the primary source material. I've also exported to linear 16bit tiff files and am seeing some degradation as well so possibly it's due to the import. Suffice to say, I think this needs to be addressed if there is a loss of data.